Yeah, the card/paper/tissue trick definitely does not work for me either. I can't imagine how it works for anyone, actually.
I use plain, ordinary store-bought countersinks. I can file the screw heads to match the bevel angle easily enough. I turn them by hand in a brace, and I use two different ones. A three flute, and a five flute, changing them up every few turns, so they each cancel each other out, and I don't get a chatter started.
Old countersinks, I am told, were cut by hand and had unevenly spaced flutes, so chattering was not a problem.